By Jacques Lafontaine
This booklet is an advent to differential manifolds. It offers sturdy preliminaries for extra complex issues: Riemannian manifolds, differential topology, Lie thought. It presupposes little heritage: the reader is simply anticipated to grasp simple differential calculus, and a bit point-set topology. The booklet covers the most subject matters of differential geometry: manifolds, tangent house, vector fields, differential types, Lie teams, and some extra refined themes equivalent to de Rham cohomology, measure thought and the Gauss-Bonnet theorem for surfaces.
Its ambition is to provide strong foundations. particularly, the creation of “abstract” notions akin to manifolds or differential kinds is stimulated through questions and examples from arithmetic or theoretical physics. greater than one hundred fifty routines, a few of them effortless and classical, a few others extra subtle, can assist the newbie in addition to the extra professional reader. strategies are supplied for many of them.
The publication could be of curiosity to numerous readers: undergraduate and graduate scholars for a primary touch to differential manifolds, mathematicians from different fields and physicists who desire to collect a few feeling approximately this pretty theory.
The unique French textual content advent aux variétés différentielles has been a best-seller in its class in France for lots of years.
Jacques Lafontaine was once successively assistant Professor at Paris Diderot college and Professor on the college of Montpellier, the place he's almost immediately emeritus. His major examine pursuits are Riemannian and pseudo-Riemannian geometry, together with a few points of mathematical relativity. along with his own examine articles, he was once concerned about numerous textbooks and study monographs.
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An Introduction to Differential Manifolds by Jacques Lafontaine